How to calculate EMI?

EMI Calculation

In our daily life we face enormous application of mathematics. Calculation of equated monthly installments (EMI) for car or home loan is one such common application of mathematics.

EMI or equated monthly installments is the most popular form of loan payment. It is a fixed amount of repayment made every month towards the loan, which includes payment towards both principal and interest. Most of us always believe the bank executives blindly on the figure which they quote as EMI.

This post is to explain the mathematics behind EMI and how to calculate it in excel using inbuilt excel function. If you wish to learn shortcut to find the time required to double a sum of money invested at certain rate of interest, you can apply Rule of 72.

EMI Calculation Formula

Here P = principal amount (loan taken)

r = interest rate per month (ex: if interest rate per annum is 10% then 10/(12*100))

n= tenure in months

For example,

EMI = 100000*0.01*(1+0.01)^24 /((1+0.01)^24 -1) = 4707

Where,

p = loan taken = 1,00,000

r = interest rate per month = 1% = 0.01

n= tenure in months = 2 Years = 24 months

This formula assumes, EMI payment is made at the end of each period (month). This is also called EMI in arrears. If EMI is paid at the beginning of each period it is called EMI in advance.

Further additions will be done on EMI for any other processing fee or possible charges which may be applicable as per the rules of financing institutions (bank).

Calculation of EMI in excel

In excel it is very simple to calculate EMI. There is an inbuilt formula for EMI calculation called PMT

PMT(rate,nper,pv)

Where,

Rate – Interest rate for the loan.

nper – Total number of payments for the loan.

PV – Present value/principal or loan taken.

FV – Future value (you can omit it)

Type – we have to put the value either 0 or 1. If payments are made at the beginning (EMI in advance) of each period, 1 is used. If EMI payments are made at the end of the period (EMI in arrears) put 0. If omitted 0 is taken a default value. Just open a new excel file and try it yourself.

Lot more can be discussed about EMI. Please share your knowledge, doubts or experiences with EMI calculations by posting comments below.

Is there any manual formal available for calculating rate of interest if I have total loan amount, monthly installment amount & tenure. Example, 2875000 loan amount repaid by 360000/-per month for 10 months. Then how calculate manually the rate of interest included in this transaction.
Thank You.

Is there any manual formal available for calculating rate of interest if I have total loan amount, monthly installment amount & tenure. Example, 2875000 loan amount repaid by 360000/-per month for 10 months. Then how calculate manually the rate of interest included in this transaction.
Thank You.

Respected sir,
i am Balaji M i want to know how to calculate emi for
p = 100000
Roi= 12%
N= 12 months
in that i want what is the short cut to calculate (0.01)^12, detailed step i need so that i can proceed further otherwise i have to calculate like 0.01*0.01*0.01………like wise 12 times so plz guide with detailed steps

Dear Sir,
I calculated as you showed. But on SBI website I calculated with their EMI calculator which is different. I calculated on principal 1000000, Interest rate 9.75% and 180 months of tenure. With your formula I obtain EMI Rs. 97500 but on SBI site it is shown Rs. 10516.99. Here is the link https://www.sbi.co.in/portal/web/home/emi-calculator

The Mathematical formula for calculating
EMI = [P x R x (1+R) ^n] / [(1+R)^ n-1].
P is the principal loan amount,
R rate of interest per month and
N is the the number of monthly installments).
Manual calculations are too complicated to perform accurately, which is why many borrowers are left confused after availing a loan. Understanding this pain-point led BankBazaar to develop one of the easiest and most user-friendly online Loan EMI Calculators.

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As mentioned in the post, while putting down the EMI formula (PMT) in excel, we’ve to mention TYPE – here we have to put the value either 0 or 1. If payments are made at the beginning (EMI in advance) of each period, 1 is used. If EMI payments are made at the end of the period (EMI in arrears) put 0. If omitted 0 is taken a default value.

I have Found out a new formula for this to do, not only this we can do lot or all calculations relating to EMI calculator, I think you did not visited my Blog please visit and Download my new type of EMI Calculator

Main thing in this blog is my New Type of EMI Calculator download it, if you do not download the EMI calculator wast of visiting my Blog, I have given so many links on the top of my blog all are same, so download from any one of the link and one more thing if you see the Normal Formula for calculating which i have given in the blog it is totally different formula because i have found out the formula again which is already exist instead of taking the existing formula from books or Website

Just Download EMI Calculator from this link: http://emicalculator3types.blogspot.in/
and select 3 rd type of EMI Calculator in downloaded software, you will get Answer, if any doubts please contact me.

I had a bad experience with a bank. Out of the total amount refunded every year, they were bifurcating it into principal refund and interest refund. Per year their interest was about Rs 10000/= more than what it should have been. I persisted with my calculation and after many months they admitted that there was a bug in their software and thanked me for getting hold of it.
Better to be careful with the calculations.

I had suggested a thumb rule which is quite useful in comparing different loan propositions and possible EMI.

The thumb rule is
EMI is slightly more than P * (r/2 + 1/n) where P = principal, r = rate of interest per month, n = number of months.

Respected Sir,
Actually sir i am working a MFI , our repayment is EMI but i am not understand , onward 2 years above but i am not know about emi formula means how to calculate if you help me i will very happy to you ( My No-7873262455)